Question

Find the amount and compound interest when the interest is compounded
annually.

i) Principal = Rs 5000, Time = 3 years,Rate = 5% per annum

ii) Principal = Rs 2000,Time = 2 years,Rate = 8% per annum

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Answer 1

Answer:

Formulas used in this question :

$\boxed{ \sf \purple{Amount = \green{P \: \bigg[1 \: + \: \dfrac{R}{100} \bigg]^{n} }}}$

$\boxed { \sf \purple {Compound \: interest \: = \green{ \: Amount \: - \: Principal }} }$

Solution : 1

$\bf \red{Given \: : }$ ↴

$\sf \: Principal \: : \: Rs. 5000$

$\sf \: Time \: : \: 3 \: years$

$\sf \: Rate \: : \: 5 \: \%$

$\bf \: \red{To \: find \: : }$ ↴

$\sf We \: have \:to \:find \:the \:amount\: and \:CI.$

$\bf \red{So, \: Let's \: Start : }$ ↴

$\sf Amount = 5000 \: \bigg[1 \: + \: \dfrac{5}{100} \bigg]^{3}$

$\sf Amount = 5000 \: \bigg[1 \: + \: \dfrac{1}{20} \bigg]^{3}$

$\sf Amount = 5000 \: \bigg[ \dfrac{20 + 1}{20} \bigg]^{3}$

$\sf Amount = 5000 \: \times \: \dfrac{21}{20} ^{3}$

$\sf Amount = 5000 \: \times \: \dfrac{9261}{8000}$

$\sf Amount = 5 \: \times \: \dfrac{9261}{8}$

$\sf Amount = \dfrac{46305}{8} \: = \red{Rs. \: 5788.125}$

$\sf \: CI = \: 5788.125 \: - \: 5000 \: = \: \red{Rs. \: 788.125 }$

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Solution - 2

$\bf \red{Given \: : }$ ↴

$\sf \: Principal \: : \: Rs. 2000$

$\sf \: Time \: : \: 2\: years$

$\sf \: Rate \: : \: 8 \: \%$

$\bf \: \red{To \: find \: : }$ ↴

$\sf We \: have \:to \:find \:the \:amount\: and \:CI.$

$\bf \red{So, \: Let's \: Start : }$ ↴

$\sf Amount = 2000 \: \bigg[1 \: + \: \dfrac{8}{100} \bigg]^{2}$

$\sf Amount = 2000 \: \bigg[1 \: + \: \dfrac{2}{25} \bigg]^{2}$

$\sf Amount = 2000 \: \bigg[ \: \dfrac{25 + 2}{25} \bigg]^{2}$

$\sf Amount = 2000 \: \times \: \dfrac{27}{25} ^{2}$

$\sf Amount = 2000 \: \times \: \dfrac{729}{625}$

$\sf \: So, \: the \: amount \: = \red{ Rs. \: 2332.8 }$

$\sf \: CI = \: 2332.8 \: - \: 2000 \: = \: \red{Rs. \: 332.8 }$